Toeplitzmult script description:

Publisher review:Toeplitzmult implements fast matrix-vector multiplication for Toeplitz matrices. This directory contains MATLAB functions for the fast multiplication of a Toeplitz matrix times a vector. By using these routines you can avoid storing the entire matrix (using two vectors of lenght n rather than a matrix of size n*n), and also dramatically speedup the multiplication. The algorithm used here runs in O(n*log(n)) time instead of the O(n^2) time required by conventional matrix multiplication.The simplest case involves the multiplication of a Toeplitz matrix times a single vector. To multiply toeplitz(a,b) times x, use>> y=toeplitzmult(a,b,x) If you have a single matrix that will be multiplied times many vectors, then use>> F=toeplitzmultaux(a,b);>> y1=toeplitzmult2(F,x1);>> y2=toeplitzmult2(F,x2);>> y3=toeplitzmult2(F,x3);...The script example.m demonstrates the use of these functions.Note that this code works correctly with matrices and vectors that are real or complex. However, due to round-off errors, the product might have a small imaginary component even though a,b, and x are all real. To correct this, simply usereal(toeplitz(a,b,x))A good introduction to how these algorithms work can be found in the book "Matrix Computations, 3rd ed." by Golub and Van Loan. Requirements: · MATLAB Release: R14SP2

Google Chrome version 42 comes with implementation of interesting options for software developers who want to turn their websites into complex Web applications: Push notification system which is permanently active.

The Windows 10 preview event brought also to the attention of gamers a demonstration of the advantages of the new DirectX 12 API by Microsoft, which announced several technologies providing integration with Xbox One game consoles.